Answer is obvious: Yes. Then, we can add some differences between the main "proto" death metal scenes:
FLORIDA: Thrash and first death metal bands are contemporaries. Chuck started like Mantas (pre-Death) in 1984 and they sounded thrash metal with growls. "Agressive tyrant" demo from Massacre exactly the same. Listened Executioner demo (pre Xecutioner, pre Obituary) it´s not death metal, they evolved after that. When they started to add an "evil" sound influenced by Celtic Frost and Possessed mainly it became death metal (Death, Morbid Angel, Deicide)
GREAT BRITAIN: The crust and hardcore scene influenced some bands. I´m not talking about Napalm Death or Carcass that started in grind core but Bolt Thrower, for instante. If you listen their early demos or "In battle there´s no law" you can find more Discharge and Extreme Noise Terror elements than from Metallica.
SWEDEN: Mmm... Sweden or Stockholm is different. In relation to Florida scene the mixed (in my opinion) european and US thrash metal in order to get more intensity in their sound. In the beginning not so well played as Morbid Angel or Death but rawer. Just like Metallica or Slayer Vs Kreator and Sodom I guess.
BRASIL: For me, the "real" transition between styles. Not only Sepultura, we got Sarcofago, Vulcano and all those crazy bands. They much more "european" than the swedes. They sounded like Sodom, Destruction or Kreator in a cave.